Solar Supergranulation and two-dimensional Hydrodynamic Turbulence

Abstract

In a two-dimensional incompressible fluid, the total energy as well as the total squared vorticity called enstrophy is conserved. It is found that the energy spectrum in two-dimensional hydrodynamic turbulence cascades to smaller wave numbers in the presence of viscous dissipation and therefore the energy is expected to accumulate at the longest wavelength that the system allows. The enstrophy on the other hand cascades to shorter wavelengths and is continuously dissipated. This conclusion is reached by finding the initial range of the turbulent spectrum. However, even the absence of dissipation, one can show that the energy spectrum condensates to largest scale as a consequence of conservation of energy and enstrophy during the cascade through the nonlinear term [(V. V)V]. it is found that if the enstrophy vanishes then the total energy remains constant even the presence of dissipation. Thus the system evolves to a state of minimum enstrophy with constant energy. The observed two dimensional nature of the velocity fields in super granulation permits us to make use of the characters of two dimensional hydrodynamic turbulence. Thus it is proposed that super granulation is proposed is produced from granulation by the selective decay process in which the energy tends to accumulate at the largest scale is determined from the ratio of energy to enstrophy and presumably determines the scale of the solar super granulation. Inclusion of magnetic field will take us to magneto-Hydrodynamic turbulence which also permits the formation of organized structures.